Universal oscillations in counting statistics

C. Flindt*, C. Fricke, F. Hohls, T. Novotný, K. Netočný, T. Brandes, R. J. Haug

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

167 Citations (Scopus)


Noise is a result of stochastic processes that originate from quantum or classical sources. Higher-order cumulants of the probability distribution underlying the stochastic events are believed to contain details that characterize the correlations within a given noise source and its interaction with the environment, but they are often difficult to measure. Here we report measurements of the transient cumulants «nm» of the number n of passed charges to very high orders (up to m = 15) for electron transport through a quantum dot. For large m, the cumulants display striking oscillations as functions of measurement time with magnitudes that grow factorially with m. Using mathematical properties of high-order derivatives in the complex plane we show that the oscillations of the cumulants in fact constitute a universal phenomenon, appearing as functions of almost any parameter, including time in the transient regime. These ubiquitous oscillations and the factorial growth are system-independent and our theory provides a unified interpretation of previous theoretical studies of high-order cumulants as well as our new experimental data.

Original languageEnglish
Pages (from-to)10116-10119
Number of pages4
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number25
Publication statusPublished - 2009
MoE publication typeA1 Journal article-refereed


  • Cumulants
  • Distributions
  • Electron transport
  • Noise and fluctuations

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